Heat 1 tablespoon of vegetable oil in a large wok or skillet over medium-high heat. Add the diced carrot and green beans, cooking for 3-4 minutes until slightly tender. Push the vegetables to one side of the pan.
2
In the cleared side, add the remaining oil and crack in the eggs (if using). Scramble until just cooked, then mix with the vegetables.
3
Add the cooked rice to the pan, breaking up any clumps. Stir well to combine all ingredients.
4
Pour soy sauce and sesame oil (if using) over the rice mixture and stir to evenly distribute. Season with salt and pepper to taste.
5
Cook for an additional 3-5 minutes, stirring frequently, until heated through. Garnish with chopped green onions if desired. Serve hot.